Toeplitz Quotient C*-Algebras and Ratio Limits for Random Walks

Adam Dor-On

doi:10.25537/dm.2021v26.1529-1556

Toeplitz Quotient C*-Algebras and Ratio Limits for Random Walks

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Abstract

We study quotients of the Toeplitz C*-algebra of a random walk, similar to those studied by the author and Markiewicz for finite stochastic matrices. We introduce a new Cuntz-type quotient C*-algebra for random walks that have convergent ratios of transition probabilities. These C*-algebras give rise to new notions of ratio limit space and boundary for such random walks, which are computed by appealing to a companion paper by Woess.

Original language	English
Pages (from-to)	1529-1556
Number of pages	28
Journal	Documenta Mathematica
Volume	26
DOIs	https://doi.org/10.25537/dm.2021v26.1529-1556
State	Published - 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021, Documenta Mathematica.All Rights Reserved.

Keywords

Cuntz algebras
Gauge-invariant uniqueness
Martin boundary
Random walks
Ratio limit boundary
Strong ratio limit property
Subproduct systems
Symmetry equivariance
Toeplitz quotients

ASJC Scopus subject areas

General Mathematics

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10.25537/dm.2021v26.1529-1556

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KW - Gauge-invariant uniqueness

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KW - Strong ratio limit property

KW - Subproduct systems

KW - Symmetry equivariance

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Toeplitz Quotient C*-Algebras and Ratio Limits for Random Walks

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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